Terminology for conversions among 3 major Christian branches

"Crossing the Tiber" / "Swimming the Tiber" have come to be the shorthand term for converting to Roman Catholicism, as well as "Swimming/Crossing the Thames" for converting to Anglicanism. (source [*Wikipedia*](https://en.wikipedia.org/wiki/Tiber#History)) I wonder whether there are swimming/crossing bodies of water related terms for conversion between other branches of Christianity, especially to/from Eastern Orthodoxy? How about for conversion among Protestant branches?